Multiplying Polynomials

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MultiplyingPolynomials

• Distribute and FOIL

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Polynomials Polynomials
Multiplying a Polynomial by another Polynomial
requires more than one distributing step.
Multiply (2a 7b)(3a 5b)
Distribute 2a(3a 5b) and distribute 7b(3a
5b)
6a2 10ab
21ab 35b2
Then add those products, adding like terms
6a2 10ab 21ab 35b2
6a2 31ab 35b2
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Polynomials Polynomials
An alternative is to stack the polynomials and do
long multiplication.
(2a 7b) x (3a 5b)
(2a 7b)(3a 5b)
(2a 7b) x (3a 5b)
Multiply by 5b, then by 3a
When multiplying by 3a, line up the first term
under 3a.
21ab 35b2
6a2 10ab

Add like terms
6a2 31ab 35b2
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Polynomials Polynomials
Multiply the following polynomials
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Polynomials Polynomials
-x -5
2x2 10x
2x2 9x -5
-15w 10
6w2 -4w
6w2 -19w 10
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Polynomials Polynomials
2a2 a -1
4a4 2a3 -2a2
4a4 2a3 a -1
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Types of Polynomials

• We have names to classify polynomials based on
  how many terms they have
• Monomial a polynomial with one term
• Binomial a polynomial with two terms
• Trinomial a polynomial with three terms

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F.O.I.L.
There is an acronym to help us remember how to
multiply two binomials without stacking them.
(2x -3)(4x 5)
F Multiply the First term in each binomial. 2x
4x 8x2
O Multiply the Outer terms in the binomials. 2x
5 10x
I Multiply the Inner terms in the binomials. -3
4x -12x
L Multiply the Last term in each binomial. -3
5 -15
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F.O.I.L.
Use the FOIL method to multiply these binomials
1) (3a 4)(2a 1) 2) (x 4)(x - 5) 3) (x
5)(x - 5) 4) (c - 3)(2c - 5) 5) (2w 3)(2w - 3)
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F.O.I.L.
Use the FOIL method to multiply these binomials
1) (3a 4)(2a 1) 6a2 3a 8a 4 6a2
11a 4 2) (x 4)(x - 5) x2 -5x 4x -20
x2 -1x -20 3) (x 5)(x - 5) x2 -5x
5x -25 x2 -25 4) (c - 3)(2c - 5) 2c2
-5c -6c 15 2c2 -11c 15 5) (2w 3)(2w
- 3) 4w2 -6w 6w -9 4w2 -9